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On two numerical methods for homogenization of Maxwell's equations

Engström, Christian LU and Sjöberg, Daniel LU (2007) In Journal Electromagnetic Waves and Applications 21(13). p.1845-1856
Abstract
When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal Electromagnetic Waves and Applications
volume
21
issue
13
pages
1845 - 1856
publisher
VSP BV
external identifiers
  • wos:000250206800010
  • scopus:34547303103
ISSN
1569-3937
DOI
10.1163/156939307781891076
language
English
LU publication?
yes
id
46c43c4d-fe23-4f16-a89e-e424c291d6b3 (old id 637534)
date added to LUP
2007-12-03 15:30:51
date last changed
2017-05-21 03:32:50
@article{46c43c4d-fe23-4f16-a89e-e424c291d6b3,
  abstract     = {When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.},
  author       = {Engström, Christian and Sjöberg, Daniel},
  issn         = {1569-3937},
  language     = {eng},
  number       = {13},
  pages        = {1845--1856},
  publisher    = {VSP BV},
  series       = {Journal Electromagnetic Waves and Applications},
  title        = {On two numerical methods for homogenization of Maxwell's equations},
  url          = {http://dx.doi.org/10.1163/156939307781891076},
  volume       = {21},
  year         = {2007},
}